THE PRINTING OF MATHEMATICS THE PRINTING OF MATHEMATICS AIDS FOR AUTHORS AND EDITORS AND RULES FOR COMPOSITORS AND READERS AT THE UNIVERSITY PRESS, OXFORD By T. W. CHAUNDY University Reader in Mathematics P. R. BARRETT Mathematical Reader at the University Press, Oxford and CHARLES BATEY Printer to the University OXFORD UNIVERSITY PRESS LONDON: GEOFFREY CUMBERLEGE 1954 Math. - Econ. Oxford University Press, Amen House, London E.C.4 2 GLASGOW NEW YORE TORONTO MELBOURNE WELLINGTON BOMBAY CALCUTTA MADRAS KARACHI CAPE TOWN IBADAN MA 00. G Geoffrey Cumberlege, Publisher to the University 3 C 4 8 PRINTED IN GREAT BRITAIN Matf, - E aan biathe St Ot ys \ 7 21.64 Boe PREFACE ALTHOUGH mechanical composition had become firmly established in printing-houses long before 1930, no significant attempt had been made before that time to develop the resources of the machine, or adapt the technique of the machine compositor, to the exacting demands of mathe- matical printing. In that year thefirst serious approach to the problem was made at the University Press in Oxford. The early experiments were made in collaboration with Professor G. H. Hardy andProfessor R. H. Fowler, andtheeditors of the Quarterly Journal of Mathematics (for which these first essays were designed) and with the Monotype Corporation. Much adaptation and recutting of type faces was necessary before the new system could be brought into use. These joint preparations included the drafting of an entirely new code of ‘Rules for the Composition of Mathematics’ which has been reserved hitherto for the use of compositors at the Press and those authors and editors whose work was produced under the Press imprints. It is now felt that these rules should have a widercirculation since, in the twenty years which haveintervened, they have acquired a greatersignificance. The reasons for this are well known. The end of the War not only released many scientific papers for publication, but found us with much research in progress and many mathematicians and scientists offering the results of their work to a larger scientific public anxious to read it. These demands were made upona printing industry already struggling to meet greatly increased calls upon its services whenit wasitself suffer- ing from the reduction of its mechanical capacity by air raids, from the paperscarcity, and, most importantofall, from theloss of skilled crafts- men. The learned societies and the printing-trade organizations have sought a remedyfor this situation by persuading moreprinters to under- take mathematical printing. These printers may have producedlittle work of the kind before, and almost certainly nothingin this field, which is known in the trade as ‘higher mathematical printing’. Theoriginal ‘Rules’, themselves amendedby continuoustrial and rich experience, are here preceded by two new chapters. Thefirst chapteris a simple explanation of the technique of printing and is addressed to those authors who are curious to know how their writings are trans- formed to the orderliness of the printed page; the second chapter, begun as the offering of a mathematical author andeditorto his fellow- workers in this field, culled from notes gathered over many years, has vi PREFACE endedin closest collaboration with the reader whofor as many years has reconciled the demandsof author, editor, and printer; the third chapter is the aforesaid collection of ‘Rules’ and is intended for compositors, readers, authors, and editors. Appendixes follow on Handwriting, Types available, and Abbreviations. It is not expected that anyone will read this book from cover to cover, but it is hoped that both author andprinter will find it an acceptable and ready work of reference. The authors wish to emphasize that the rules of style set out here reflect the Oxford practice. We know of other authorities, both in this country and abroad, and, where wediffer from them, we do so deliberately for reasons which webelieve to be good reasons. We acknowledge gratefully the help of many authors and editors whose advice andcriticism are reflected here. We also thank the Mono- type Corporation for their assistance in providingillustrations. It is hoped that this book will not only help the printer, but will assist the enlarged company of authors to understand the technical problems which are peculiar to the composition of mathematics, so that they can ease the printer’s task and their own. We hope, aboveall, that the publication of these ‘Rules’ may help to standardize the techniques of both writer and printer. The authors would welcomeanycriticisms or suggestions calculated to increase the usefulness of this work. . W.C. s W .R. B. Q December 1953 .B. CONTENTS LIST OF ILLUSTRATIONS ix I. THE MECHANICS OF MATHEMATICAL PRINTING 1 II. RECOMMENDATIONS TO MATHEMATICAL AUTHORS 1, INTRODUCTION 21 2. FRACTIONS 26 3. SURDS 29 4. SUPERIORS AND INFERIORS 30 5. BRACKETS ' 32 6. EMBELLISHED CHARACTERS 35 7. DISPLAYED FORMULAE -36 8. NOTATION (MISCELLANEOUS) 40 9. HEADINGS AND NUMBERING 44 10. FOOTNOTES AND REFERENCES 48 11, VARIETIES OF TYPE 51 12. PUNCTUATION 54 13. WoRDING 59 14. PREPARING COPY 65 15. CORRECTION OF PROOFS . 70 16. FINAL QUERIES AND OFFPRINTS 73 III. RULES FOR THE COMPOSITION OF MATHEMATICS AT THE UNIVERSITY PRESS, OXFORD 74 APPENDIXES A. LEGIBLE HANDWRITING 90 B. Type SPECIMENS AND LIsT OF SPECIAL Sorts 91 99 C. ABBREVIATIONS INDEX 102 LIST OF ILLUSTRATIONS FIGURES 1. Specimens of single type 2 2. Spaces showing the build-up and justification of pieces of formulae 3. ‘Monotype’ matrices 4, The ‘Monotype’ mould PLATES 1. A compositor at work 11. The matrix-case 111. A ‘Monotype’ keyboard between pages 8 and 9 . A ‘Monotype’ casting machine IV v. The ‘Monotype’ keyboard arrangement for mathematical composition I. THE MECHANICS OF MATHEMATICAL PRINTING THE HAND COMPOSITOR The letterpress method of printing THEREare (broadly) three methods ofprinting: letterpress, lithographic, and gravure; we are concerned here only with the first-named. The letterpress method is based on type, which provides a printing surface cast in substantial relief; hence it is also known as the‘relief’ process of printing. Type is cast in moulds: for hand-composition each character is cast separately in quantity and placed in trays (known as ‘cases’) which are subdivided to provide a little box for each letter, figure, or symbol. In mechanical composition each character may be selected and cast separately and assembled into words and sentences by machine, as in the ‘Monotype’ method; or the separate matrices may themselves be assembled in a line of complete words with spaces and the whole cast as a thin and solid block of metal (known as a ‘slug’), as in the Linotype system, used mostly in newspapers and ordinary bookwork. The com- plications of mathematical printing demand the greater flexibility of movable types, and so this work is normally set either by hand or, increasingly, on a ‘Monotype’ machine. The nature of type Let us look at the type shown in Fig. 1 (a). This drawing represents a single type of the capital M standing upright upon its feet as it would — when being printed alongside its fellows. The distance from the feet to the ‘face’ (which is the printing surface) is a fixed dimension of 0-918 inch and is known asthe ‘height-to-paper’ or just ‘type height’.+ All the types of every fount used in a printing-house, and all the blocks, must be provided in this uniform height if they are to be assembled and printed together. The bed of the printing machine which carries the type, and the cylinder which is to apply the printing impression, are placed just this distance from one another. The distance from the front of the type to the back is known as the t This has become the standard in Great Britain, the United States, and some other countries. Continental heights vary. Oxford has retained one of these heights and casts at 0-938 inch, whichis a reflection of the early associa- tion of the Press with Dutch and French punch-cutters and type-founders. B 1597 B 2 MECHANICS OF MATHEMATICAL PRINTING ‘body size’. This dimension will be seen in Fig. 1 (a), and even more clearly in Fig. 1 (6), which is a silhouette of the type size in which this is printed. The printer defines the bodysize of his type as of so many ‘points’, a point being one seventy-second of an inch. This type is known as ‘11 point’ kecause its body measures eleven seventy-seconds of an inch. All t t a 11-point types, whether in roman oritalic, Greek or d Hebrew, will measure exactly the same. (a) (b) The width of type is variable and is determined by the Fra. 1. shape of the character represented: x may besaid to be of average width, while M is one of the wider characters, and f one of the narrower. It should also be noted that the different characters occupy varying proportions of the body size: thus the small X occupies a space which is approximately in the centre of the body, but the capital M being an ascendingletterfills the centre and top, while the italic f, being a letter which both ascends and descends, occupies almostall the depth available. The indentation in the front of the type whichis clearly shown in Fig. 1 is the ‘nick’, whose use will appearlater. Composing type by hand Weshall better understand the complexities of machine composition, particularly of mathematics, if we first look over the shoulder of a hand compositor at work. He stands before a high desk whichis, in fact, a printer’s ‘frame’. On top of the frame and sloping towards him are type cases in pairs, and there are mostlikely two pairs. The bottom andnearer case will contain the small letters of the alphabet (which explains why the printer always refers to these as ‘lower case’, usually abbreviated to ‘le.’ on proofs), and other material most commonly required, such as spaces, punctuation marks, and figures. The top case is known as the ‘upper case’ and holds capitals, small capitals, and other types in less frequent demand. The compositor holds a metal tool in his left hand which he will refer to as his ‘stick’, so called because the early printer constructed it of wood. This is a piece of thin but rigid steel which may be 6 inches long and about3 inches broad, havingfixed flanges somewhatless than type height on two adjacent sides, and a movable flange on another. The com- positor’s first care is to adjust this movable flange to the width of the pages he is to compose. The unit of measurementfor this purposeis the 12-point em, which was originally the capital M and wasselected because it was a square of the bodysize in some founts (but by no meansinall). MECHANICS OF MATHEMATICAL PRINTING 3 The compositor maystill use this letter, or the ‘square’ space known as the ‘em’, to set his stick. At this stage you should also be introduced to the ‘en’, which is half an em in width. Both units will be mentioned frequently in this guide: their derivation should now beclear. The book to be composed maybe of 20 or 30 ems or of any other reasonable width; the page you are readingis of 27 ems. This dimension is always referred to as the ‘measure’. The compositor, then, assembles the proper and predetermined numberof emsin his stick, and fixes the movableflange so that it presses tightly against this line. Having removed the line of ems, he may begin composition. Here I should explain that the compositor has an auxiliary aid known as the ‘setting rule’. This is a thin strip of brass, cut to the exact length of the measure in which heis to set, and of the same height as the type. The setting rule is placed in the stick and presents a smooth surface which facilitates the assembly of the letters. So with his ‘copy’ before him, usually propped up on the lower part of the upper case, the compositor gathers type from his case letter by letter. He picks up each type with his right hand andputs it in his stick face outwardsand with nick showing(see Fig. 1), which provesit properly disposed to print the right way up, holding it in place with the thumb of his left hand the while (see Plate I). As each word is completed he adds a space, and so proceeds until he can get no other word in theline, after whichhe adjusts the spaces until theline is tight. Here he has two cares: first the spaces must be evenly distributed to ensure that the complete page as eventually printed has an even pattern with no unsightly gaps; and secondly thatall his lines are of an even tightness so that each type in each page in a series of pages will be held firmly against the hazards of transport and proofing, and inking andprinting at speed on machine. Having spacedtheline to his satisfaction, the compositor removes the setting rule (on which theline of type has been resting) and, placing it over the completed line in his stick, is ready to continue setting. At this point I should makeit clear that the techniques I am describing, though ancient, are not archaic. Booksare rarely set by hand, it is true, but all the major corrections and adjustments necessary to single-type machine-composedtypes, all principal headings, and muchelse, still pass through the compositor’s stick. This simple tool, and the case and the frame, arestill essential to the printer, particularly if it is his business to print mathematics. But to return to our hand compositor: if he is composing mathematics he maybecalled uponto build up the pieces of a formula,for instance,